1. Field of the Invention
The present invention relates to a solid-state laser apparatus, and in particular to a small-sized, mode-locked solid-state laser apparatus which has high output power, and enables highly efficient, short-pulse generation.
2. Description of the Related Art
Conventionally, efforts of developing solid-state lasers in which a solid-state laser medium (e.g., a laser crystal, ceramic substance, glass, or the like) doped with rare-earth ions or transition-metal ions is excited with a semiconductor laser (laser diode (LD)) as an excitation light source have been actively made. Among others, a wide variety of applications of the short-pulse lasers, which emit the so-called short light pulses (having the durations on the order of picoseconds to femtoseconds), have been searched for and proposed, and part of such applications have been put into practical use after verification.
In the short-pulse lasers, the short light pulses are generated by an operation called mode locking. The mode locking is a technique of making a great number of longitudinal-mode laser oscillations in phase (i.e., making the phase differences between the longitudinal-mode laser oscillations zero) so as to produce pulses having very small durations in the time domain by multimode interference between the longitudinal-mode laser oscillations. In particular, for the solid-state lasers, the mode locking using the semiconductor saturable absorbing mirror (SESAM) is advantageous since the SESAM can realize solid-state lasers which are simple in structure, low in cost, and small in size, and the mode locking automatically starts in the solid-state lasers using the SESAM. Therefore, efforts of studying and developing the mode locking using the SESAM have been vigorously made.
Especially, the soliton mode locking, which is a type of mode locking, enables generation of pulses having the durations on the order of femtoseconds by a combination of negative group-velocity dispersion in the laser resonator and self-phase modulation, which mainly occurs in the laser medium. More specifically, in the soliton mode locking, the SESAM starts the mode locking and maintains and stabilizes generation of pulses, and the negative group velocity dispersion and the self-phase modulation are balanced so as to produce soliton pulses and steepen the mode-locked pulses. Thus, the soliton mode locking enables stable pulse generation. (The soliton mode locking is defined, for example, in F. Brunner et al., “Diode-pumped femtosecond Yb:KGd(WO4)2 laser with 1.1-W average power”, Optics Letters, Vol. 25, No. 15, pp. 1119-1121, 2000, and C. Hönninger et al., “Q-switching stability limits of continuous-wave passive mode locking”, Journal of the Optical Society of America B. Vol. 16, No. 1, pp. 46-56, 1999.)
The solid-state laser apparatus realizing the soliton mode locking is basically configured by arranging in a resonator a solid-state laser medium, a saturable absorbing mirror, and a negative dispersion element (negative group-velocity dispersion element).
FIG. 18 illustrates a typical configuration of a conventional mode-locked, Yb-doped solid-state laser, which is disclosed in the Brunner reference, where the solid-state laser medium is Yb:KGd (WO4)2. In FIG. 18, reference number 80 denotes a pair of excitation light sources, 81 denotes a pair of input optical systems, 83 denotes a solid-state laser medium, M1 and M2 denote a pair of concave mirrors, 84 denotes a concave mirror, 85 denotes an SESAM, 86 and 87 denote a pair of prisms, 88 denotes knife-edge plates, and 89 denotes an output coupler. The pair of excitation light sources 80 emit excitation light having the wavelength of, for example, 980 nm. The input optical systems 81 are respectively arranged in association with the excitation light sources 80. The concave mirrors M1 and M2 have a curvature radius of, for example, 20 cm, and constitute a resonator. The concave mirror 84 has a curvature radius of 20 cm. The prisms 86 and 87 are made of, for example, SF10 glass. The output coupler 89 has a transmittance of, for example, 4.3%.
Generally, in the mode-locked solid-state laser apparatuses having a configuration as above, the beam in resonator is condensed by each of the concave mirrors M1, M2, and 84 in order to reduce the spot size (i.e., the mode radius ωL) of the oscillating light in the laser medium and the spot size (i.e., the mode radius ωA) at the SESAM. The spot sizes in the laser medium and the SESAM are reduced for the first purpose of lowering the threshold for laser oscillation (laser oscillation threshold) and the second purpose of satisfying a condition for soliton mode locking.
The first purpose (of lowering the laser oscillation threshold) is explained below.
The laser oscillation threshold Pth is expressed by the formula,
                              P          th                =                                            π              ⁢                                                          ⁢                                                hv                  P                                ⁡                                  (                                                            ω                      L                      2                                        +                                          ω                      P                      2                                                        )                                                                    4              ⁢              σ              ⁢                                                          ⁢                                                τη                  a                                ⁡                                  (                                                            f                      1                                        +                                          f                      2                                                        )                                                              ⁢                      (                                          L                i                            +                              T                OC                            +                              2                ⁢                                  f                  1                                ⁢                σ                ⁢                                                                  ⁢                                  N                  0                                ⁢                                  l                  s                                                      )                                              (        1        )            where ωL is the beam radius of the oscillating light in the solid-state laser medium, ωP is the beam radius of the excitation light in the solid-state laser medium, hνp is the photon energy of the excitation light, σ is the stimulated-emission cross section of the solid-state laser medium, τ is the lifetime of the upper level, ηa is the absorption efficiency, f1 is the filling factor of the lower level, f2 is the filling factor of the upper level, Li is the internal loss of the resonator, T0C is the transmittance of the output mirror, N0 is the doping concentration of the rare-earth ions, and lS is the crystal length. (See T. Taira et al., “Modeling of quasi-three-level lasers and operation of cw Yb:YAG lasers”, Applied Optics, Vol. 36, No. 9, pp. 1867-1874, 1997.)
It is possible to understand, on the basis of the formula (1), that the laser oscillation threshold can be lowered by reducing the beam radius ωP of the excitation light and the radius ωL of the oscillating light in the solid-state laser medium.
The Hönninger reference reports that a Q-switching operation is mixed in the mode locking operation (i.e., a Q-switched mode locking occurs) under a certain condition in a soliton-mode-locked laser. When the Q-switched mode locking occurs, mode-locked pulses (having a frequency of 10 MHz to 1 GHz and a width on the order of picosecond to femtoseconds) are superimposed on long Q-switched pulses (having a frequency of 1 kHz to 100 kHz and a width on the order of microseconds to nanoseconds). However, generally, the Q-switched mode locking is undesirable in the applications other than the energetic use because of the instability in the output, pulse width, and pulse period. According to the Hönninger reference, a condition for preventing the Q-switching operation during the soliton mode locking by use of the saturable absorbing mirror can be expressed by the inequality,Fsat,L·Aeff,L·g·K2EP3+EP2>Fsat,L·Aeff,L·Fsat,A·Aeff,A·ΔR,   (2)where EP is the pulse energy inside the resonator, ΔR is the depth of the absorbing modulation in the saturable absorbing mirror, Fsat,A is the saturation fluence in the saturable absorbing mirror, Fsat,L(=hν/σ) is the saturation fluence in the laser medium, hν is the photon energy of the laser light, Aeff,A(=πωA2) is the oscillated-light-beam cross section at the saturable absorbing mirror, Aeff,L(=πωL2) is the oscillated-light-beam cross section in the laser medium, and g is the laser gain in the laser medium. The factor K in the inequality (2) can be expressed as,
                    K        =                                            4              ⁢              π              ⁢                                                          ⁢                              n                2                            ⁢                              l                S                                                                                    D                                            ⁢                              A                                  eff                  ,                  L                                            ⁢                              λ                0                            ⁢              Δ              ⁢                                                          ⁢                              v                G                                              ⁢                      0.315            1.76                                              (        3        )            where n2 is the nonlinear refractive index of the laser medium, D is the group-velocity dispersion (D<0) occurring in a round trip in the entire resonator, λ0 is the central wavelength of the oscillating light, and ΔνG is the gain bandwidth. It is known that the so-called CW (continuous-wave) mode locking, which is free from Q-switching instability, is realized when the pulse energy EP satisfying the condition expressed by the inequality (2) is satisfied in a resonator by reducing the oscillated-beam cross sections Aeff,A and Aeff,L. The mode-locking threshold value can be obtained as a solution EP of an equation expressed by replacing the inequality sign in the inequality (2) with an equal sign. In other words, when the pulse energy EP inside the resonator exceeds the mode-locking threshold value, the inequality (2) is satisfied.
The two conditions for the laser oscillation threshold and the (CW) mode-locking threshold value which are explained above require reduction of the oscillated-beam cross sections Aeff,A and Aeff,L in the laser medium and the SESAM. In many of the conventional mode-locked solid-state lasers, a pair of concave mirrors are arranged on both sides of the laser medium and near the SESAM so as to condense the beam. (In the example of FIG. 18, the curvature radii of the concave mirrors M1 and M2 are normally 100 to 200 nm.)
Normally, the concave mirrors M1 and M2 on both sides of the laser medium 83 are arranged at distances approximately halves of the curvature radii of the concave mirrors M1 and M2 from the laser medium 83, and the concave mirror 84 near the SESAM 85 is arranged at a distance approximately half of the curvature radius of the concave mirror 84 from the SESAM 85. Therefore, when the curvature radii of the concave mirrors are 100 to 200 mm, the necessary dimensions of the part of the solid-state laser containing the concave mirrors M1 and M2 and the laser medium 83 and the part of the solid-state laser containing the concave mirror 84 and the SESAM 85 are approximately 150 to 300 mm. Thus, in consideration of the spaces for arrangement of the other components such as the negative dispersion elements, the necessary length of the resonator becomes approximately 500 to 1000 mm. That is, the size of the solid-state laser apparatus becomes large. In the configuration of FIG. 18, the pair of prisms 86 and 87, which are distanced by 450 mm, cause negative dispersion. However, generally, solid-state laser apparatuses containing a one-meter class resonator are hard to stably operate. Therefore, the stability of the laser oscillation in the conventional solid-state laser apparatuses is low. In addition, since the conventional solid-state laser apparatuses are constituted by a great number of optical components, the cost of the conventional solid-state laser apparatuses is high.
In the above circumstances, downsizing of the mode-locked solid-state laser apparatuses is demanded for increasing the stability of the laser oscillation.
U.S. Pat. No. 7,106,764 (hereinafter referred to as U.S. Pat. No. 7,106,764) proposes a small-sized solid-state laser apparatus 100 as illustrated in FIG. 19. In the solid-state laser apparatus 100, a resonator is constituted by a solid-state laser medium 101 and a SESAM 102. The solid-state laser medium 101 and the SESAM 102 are arranged through a ring 108 so that a predetermined gap 103 is produced between the solid-state laser medium 101 and the SESAM 102. The gap 103 has the function of a GTI (Gires-Tournois interferometer) and causes negative dispersion. An end surface 104 of the laser medium 101 is a curved surface, and is coated so as to behave as an output mirror 105. Excitation light 106 is inputted and output light 107 is outputted through the output mirror 105.
Japanese Unexamined Patent Publication No. 11(1999)-168252 (hereinafter referred to as JP11-168252A) proposes provision of a chirped-mirror coating (negative-dispersion coating) on a laser medium, a saturable absorbing mirror, or an output mirror. For example, JP11-168252A proposes a small-sized laser apparatus 110 as illustrated in FIG. 20. In the laser apparatus 110, a saturable absorbing mirror 112 is formed on an end surface of a laser medium 111 by coating, so that a resonator is formed between the saturable absorbing mirror 112 and a chirped mirror 113, which is a negative-dispersion mirror. Excitation light 115 is generated by a semiconductor laser 114 and inputted into the laser medium 111, and output light 116 is outputted through the chirped mirror 113.
As explained above, U.S. Pat. No. 7,106,764 proposes downsizing of a solid-state laser apparatus by close arrangement of the solid-state laser medium and the SESAM, and JP11-168252A proposes downsizing of a solid-state laser apparatus by reduction of the number of optical components. In JP11-168252A, the number of optical components is reduced by producing the saturable absorbing mirror 112 by coating on the solid-state laser medium, and arranging the solid-state laser apparatus so that the negative-dispersion mirror is also used as the output mirror.
Although, generally, one or a combination of a pair of prisms, a pair of diffraction gratings, a negative-dispersion mirror, and the like is used as the negative dispersion element, the configuration in which the negative-dispersion mirror is also used as the output mirror (as disclosed in JP11-168252A) is desirable from the viewpoint of downsizing.
The chirped mirror and the GTI mirror are known to be a negative-dispersion mirror. For example, JP11-168252A discloses a chirped mirror which makes negative dispersion compensation (compensation with a negative dispersion) by taking advantage of the difference in light penetration between the longer wavelengths and shorter wavelengths. The GTI mirror makes negative dispersion compensation by taking advantage of optical interference occurring between a total-reflection mirror and a partial-reflection mirror.
In a typical example of the chirped mirror, high-index layers having relatively high refractive indexes and low-index layers having relatively low refractive indexes are alternately laminated in such a manner that the optical thicknesses of the high-index layers and the optical thicknesses of the low-index layers linearly vary along the thickness direction. (See, for example, R. Szipöcs et al., “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers”, Optics Letters, Vol. 19, No. 3, pp. 201-203, 1994.)
On the other hand, the GTI mirror is characterized by having a resonant structure inside a dielectric multilayer film. (See, for example, J. Kuhl and J. Heppner, “Compression of Femtosecond Optical Pulses with Dielectric Multilayer Interferometers”, IEEE Transactions on Quantum Electronics, Vol. QE-22, No. 1, pp. 182-185, 1986.) In addition, a GTI mirror having a double-GTI structure with two cavity layers arranged inside a multilayer film (as disclosed in U.S. Pat. No. 6,081,379 and a GTI mirror having a resonant structure in which no cavity layer is arranged and the optical thicknesses of multiple layers constituting a multilayer film vary in accordance with a certain rule (as disclosed in International Patent Publication No. WO00/11501) have been proposed.
Further, Japanese Unexamined Patent Publication No. 2(1990)-023302 (hereinafter referred to as JP2-023302A) proposes a dielectric multilayer-film stack which compensates for the third- or higher-order dispersion as well as the second-order dispersion. The dielectric multilayer-film stack is formed by stacking two or more dielectric multilayer films in which two or more index layers having different refractive indexes are alternately laminated, and the dielectric multilayer films have respectively different central frequencies. Japanese Unexamined Patent Publication No. 2000-138407 (hereinafter referred to as JP2000-138407A) proposes a multilayer mirror in which the outermost layers have refractive indexes respectively lower than the layers immediately below the outermost layers, and which exhibits a reflectance of 95% or higher in the visible wavelength range and causes negative group-velocity dispersion.
As explained above, in order to realize downsizing of a mode-locked solid-state laser apparatus, it is possible to consider the close arrangement of the solid-state laser medium and the SESAM and the use of the negative-dispersion mirror as an output mirror.
However, the conventional techniques explained above have the following problems.
(a) Although JP11-168252A proposes the use of the negative-dispersion mirror as the output mirror, and the negative-dispersion mirror is produced by chirped-mirror coating (having a negative dispersion function), JP11-168252A does not concretely disclose details of the negative-dispersion mirror (such as the optical transmittance, the amount of dispersion, the dielectric films constituting the negative-dispersion mirror, and the like) for use as the output mirror. That is, JP11-168252A does not disclose information necessary for realizing the negative-dispersion mirror which is produced by chirped-mirror coating and can be used as the output mirror.
(b) Although JP2000-138407A reports that the frequency chirp can be compensated for by arranging a dielectric multilayer film on the output mirror, the reflectance of the dielectric multilayer film disclosed in JP2000-138407A is 99.9% or higher, i.e., approximately 100%. That is, almost no output light can be outputted through such an output mirror. Therefore, the dielectric multilayer film disclosed in JP2000-138407A does not have a sufficient function of an output mirror.
(c) Since the magnitudes of negative dispersion caused by the commercially available negative dispersion elements are tens to hundreds of square femtoseconds, it is necessary to arrange more than one negative dispersion element in the resonator for making sufficient negative dispersion compensation. Therefore, it is difficult to achieve satisfactory downsizing and stabilization of the solid-state laser apparatus.
(d) The solid-state laser apparatuses in which the saturable absorbing mirror (as a reflection mirror) is arranged in close vicinity to or in contact with the laser medium as disclosed in U.S. Pat. No. 7,106,764 or JP11-168252A have the following problems.
As indicated in R. Paschotta et al., “Passive mode locking of thin-disk lasers: effects of spatial hole burning”, Applied Physics B, Vol. 72, No. 3, pp. 267-278, 2001, B. Braun et al., “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole burning Part I”, Applied Physics B, Vol. 61, No. 5, pp. 429-437, 1995, and F. X. Kärtner et al., “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole burning Part II”, Applied Physics B, Vol. 61, No. 6, pp. 569-579, 1995, it is known that the spatial hole burning differently occurs in the laser medium (as the gain medium) according to the position along the optical axis, is coupled to the mode locking phenomenon, and affects the stability of the mode locking.
The phase of the electric field of the optical wave jumps at the reflection mirror surfaces of the resonator, and nodes of the electric field (at which the electric field strength is zero) exist at the reflection mirror surfaces. In the case where the laser medium is arranged in close vicinity of a reflection mirror surface, the intensity of the laser wave has a stripe-like spatial distribution in the laser medium because of the phase jump at the reflection mirror surface. This phenomenon is the spatial hole burning.
The Paschotta reference reports that in the case where the laser medium is arranged in close vicinity of a reflection mirror, a dip is produced in a gain spectrum, and makes the soliton pulses traveling between the reflection surfaces in the resonator unstable. Specifically, since the hole burning effect is relatively strongly manifested in the vicinity of the reflection mirror, the gain spectrum (in the frequency domain) of the laser pulses traveling between the reflection surfaces in the resonator (which are soliton pulses having a relatively wide bandwidth) is also affected, and the gain is preferentially imparted to undesirable phenomena (such as generation of shifted pulses, double pulses, and continuous background) competing the desired pulses. Therefore, the desired soliton pulses lose in the competition, and the above undesirable phenomena make the operation of the solid-state laser apparatus unstable. Consequently, in the case where the saturable absorbing mirror (as a reflection mirror) is arranged in close vicinity to or in contact with the laser medium as disclosed in U.S. Pat. No. 7,106,764 or JP11-168252A, it is possible to consider that the spatial hole burning conspicuously occurs, and the generation of soliton pulses becomes extremely unstable. However, neither U.S. Pat. No. 7,106,764 nor JP11-168252A mentions the influence of the spatial hole burning on the mode stability, and teaches a means for realizing the mode stability.
As explained above, various proposals for downsizing of the mode-locked solid-state laser apparatuses have been conventionally made, no condition for stably generating soliton pulses in downsized solid-state laser apparatuses has been definitely proposed. In addition, no negative-dispersion mirror which can make sufficient negative dispersion compensation by itself and can also operate as an output mirror has been reported. That is, no small-sized, mode-locked solid-state laser apparatus which satisfactorily operates has been conventionally realized.